Advertisement

Functional Analysis and Its Applications

, Volume 49, Issue 3, pp 222–225 | Cite as

Representations of nilpotent groups: Extensions, neutral cohomology, and Pontryagin spaces

  • E. V. Kissin
  • V. S. Shulman
Brief Communications
  • 42 Downloads

Abstract

Spectral criteria for the cohomological triviality of extensions of representations of connected nilpotent groups are obtained. They are applied to the study of symmetrized extensions of unitary representations by finite-dimensional representations and to the theory of J-unitary representations of groups on Pontryagin spaces.

Keywords

extension of representation Pontryagin space Engel element neutral cocycle 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. S. Ismagilov, Mat. Zametki, 35:1 (1984), 99–106MathSciNetGoogle Scholar
  2. [1a]
    R. S. Ismagilov, English transl.: Math. Notes, 35:1 (1984), 55–58.zbMATHMathSciNetGoogle Scholar
  3. [2]
    R. S. Ismagilov, Izv. Akad. Nauk SSSR, Ser. Mat., 30:3 (1966), 497–522MathSciNetGoogle Scholar
  4. [2a]
    R. S. Ismagilov, English transl.: Amer. Math. Soc. Transl., II Ser., 85 (1969), 165–192.Google Scholar
  5. [3]
    A. A. Kirillov, Funkts. Anal. Prilozhen., 2:1 (1968), 96–98MathSciNetGoogle Scholar
  6. [3a]
    A. A. Kirillov, English transl.: Functional Anal. Appl., 2:1 (1968), 90–93.zbMATHMathSciNetGoogle Scholar
  7. [4]
    E. R. Kolchin, Ann. of Math., 49:1 (1948), 1–42.zbMATHMathSciNetCrossRefGoogle Scholar
  8. [5]
    M. A. Naimark, Izv. Akad. Nauk SSSR, Ser. Mat., 27:6 (1963), 1181–1185.MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.STORMLondon Metropolitan UniversityLondonUK
  2. 2.Vologda State UniversityMoscowRussia

Personalised recommendations